The cost of vaccinating an individual during an epidemic is not
constant. It is assume that it is cheaper to vaccinate the first
individuals and more expensive to vaccinate the last few individuals,
due to logistics. In this talk, I will use mathematical modeling to
compare the effects of different unit cost functions on the epidemic.
I will describe a susceptible-exposed-infected-removed (SEIR) model of
an epidemic, where susceptible individuals can be vaccinated and
removed from the epidemic. Given a particular unit cost function for
the vaccination, it is possible to determine the optimal vaccination
rate that minimizes an associated "total cost" function, using the
technique known as Pontryagin's maximum principle. Different unit
cost functions result in different optimal vaccination rates.
Pontryagin's maximum principle will be explained and several unit cost
functions will be considered.